Proving Angle Pair Relationships

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Presentation transcript:

Proving Angle Pair Relationships Geometry

If two angles form a linear pair, then they are supplementary. Linear Pair Postulate If two angles form a linear pair, then they are supplementary.

Proving Vertical Angles Theorem Given: ∠5 and ∠6 are a linear pair ∠6 and ∠7 are a linear pair Prove: ∠5 ≅ ∠7

Vertical Angles Theorem All vertical angles are congruent!

Example The measure of angle 1 is 36 degrees. Find the measures of the other three angles.

Example Solve for x and y. Then find the angle measures. (4x + 15)

Example Given that ∠G is a supplement of ∠H and m∠G = 82°, find m∠H. Given that ∠U is a complement of ∠V and m∠U = 73°, find m∠V.

Example ∠W and ∠Z are complementary. The m∠Z is five times the m∠W. Find m∠W.

Example ∠T and ∠S are supplementary. The m∠T is half the m∠S. Find m∠S.